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WEEK 2: 4 SEP THRU 10 SEP; LECTURES 4-6
Learning Objectives
Energy: Light as energy
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Describe the wave nature of light, wavelength, and frequency using the equation c = λν
What is meant by the “particle nature of light?
Calculate the energy of a photon using the equation E = hν
Be familiar with types of radiation and their relative energies in the electromagnetic spectrum (Which
have long wavelengths? Which have short? Which have high energy, which have low?)
Describe the relationship between color of visible light and its relative energy in the electromagnetic
spectrum
Describe the relationship between wavelength and energy of a photon using the equation E = hc/λ
Perform calculations involving the total energy of multiple photons using the equation ET = n(hc/λ)
Interpretation of Line spectrum
(What is happening that causes the emission lines?)
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Know that quantized emissions represent energy transitions
Be able to interpret line spectra by assigning lines to transitions
Connect line spectra to the energy of emitted photons, the color of light emitted, and its wavelength
Bohr Model of the hydrogen atom: where is the electron in the H atom?
Qualitative Goals:
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Connect the line spectrum of hydrogen to the energy level diagram of hydrogen using the Bohr model.
Define and describe the energy of an electron in the hydrogen atom
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Connect emission and absorption to pictures of electrons in orbit; We are using He ion for this goal
Have a qualitative ability to describe emission and absorption using the principal quantum number.
Know the sign of the energy change (positive or negative) when emission or absorption occurs.
Quantitative Goals
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Calculate E given ni and nf (Calculate energy of emitted photon.)
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Calculate ionization energy for H atom or He (knowing that n =  for ionization)
Know that the energy change is negative if the photon is emitted.
Orbitals: Solutions to Schrödinger equation
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What is meant by the “electron density” (or the probability of finding an electron)?
Know the qualitative meaning of wavefunctions, which are solutions to the Schrödinger Equation.
Describe the meaning of probability density, and electron density as the location of an electron.
Quantum Numbers
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Be familiar with the names of principle, angular, and magnetic quantum numbers
Define shell, subshell and orbital
Know and follow rules for allowed combination of quantum numbers
Understand the relationship between quantum numbers and size, shape, and orientation of an orbital
Know orbital names.
Describe the value of electron density in regions of space using electron density plots or contour
diagrams
Interpret an electron density plot, and define nodes and lobes of orbitals
Make connections between electron configuration and orbitals; know that quantum numbers describe
orbitals, and orbitals sufficiently describe the location of the electron
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WEEK 2: 4 SEP THRU 10 SEP; LECTURES 4-6
Homework Problems
Due: Thurs. Sept. 12
1.
A radio station broadcasts on a frequency of
99.5 kilocycles/s. What is the wavelength of this
radiation in km?
A.
B.
C.
D.
E.
2.
3.
6. The brightest emission line of an element is
420nm. What is the color of the flame?
How much energy does one mole of red
photons have? (The wavelength of red light is
725 nm.)
A.
B.
C.
D.
E.
red
yellow
green
blue
violet
Green light of wavelength 516 nm is absorbed
by an atomic gas. What is the energy difference
between the two quantum states involved in the
transition?
A.
B.
C.
D.
E.
14
5.81  10 J
3.85  1019 J
1.28  1027 J
4.29  1036 J
1.43  1044 J
−19
2.74 × 10 kJ
−46
4.56 × 10 kJ
−3
6.05 × 10 kJ
165 kJ
227 kJ
8. Which of the following statements is/are true for
the Bohr model of the hydrogen atom?
A He-Ne laser (λ = 633nm) is used to heat up a
sample. How many photons are needed to
transfer 12 J of heat to the sample?
A.
B.
C.
D.
E.
The brightest emission line in the line spectrum
of potassium is at 535nm. What is the energy of
the photon emitted?
3
7.25  10 km
7
2.99  10 km
4
2.99  10 km
3.02 km
none of these
A particular microwave photon has a
wavelength of 0.01 m, a photon of green visible
light has a wavelength of 520 nm and a photon
of gamma radiation has a wavelength of 8 pm.
Rank these forms of electromagnetic radiation in
order of increasing energy and frequency. What
7.
general trend do you see?
A.
B.
C.
D.
E.
4.
5.
19
3.8  10
12,000
11
6.3  10
3.2  1019
6
1.6  10
Week 2
1. The radius of the orbit increases as the
principal quantum number increases.
2. The energy required to ionize the atom
increases as the principal quantum number
decreases.
3. Light emitted by the excited hydrogen atom
corresponds to transitions from orbits of
higher principal quantum number to lower
principal quantum number.
A.
B.
C.
D.
E.
1 only
1and 2 only
2 and 3 only
1 and 3 only
1, 2, and 3
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WEEK 2: 4 SEP THRU 10 SEP; LECTURES 4-6
9.
In the Bohr model for the hydrogen atom, in
which orbit does an electron have higher overall
energy: n = 1 or n = 5?
10. Which of the following transitions in a hydrogen
atom results in emission of light?
i.
ii.
iii.
iv.
v.
A.
B.
C.
D.
E.
n = 3 to n = 4
n = 1 to n = 3
n = 6 to n = 4
n = 7 to n = 5
n = 2 to n = 5
13. Which quantum numbers are needed to define
the subshell?
A.
B.
C.
D.
E.
F.
n only
n and ℓ
ℓ only
mℓ only
ℓ and mℓ
n, ℓ, and mℓ
14. How many possible orbitals are there with n = 3
and m = 1?
A.
B.
C.
D.
E.
iii only
i and ii only
ii and iii only
iii and iv only
i, ii, and v
1
2
3
5
9
15. Which is not a permissible set of quantum
numbers?
11. Which of the following electron transitions in a
hydrogen atom results in the greatest release of
energy from the atom?
A.
B.
C.
D.
E.
12.
n = 3 to n = 4
n = 1 to n = 3
n = 6 to n = 4
n = 7 to n = 5
n = 2 to n = 5
Week 2
n = 2, ℓ = 0, mℓ = 0
n = 3, ℓ = 2, mℓ = 2
n = 2, ℓ = 1, mℓ = –1
n = 3, ℓ = 3, mℓ = 0
n = 4, ℓ = 3, mℓ = –3
Follow-up question: Identify the subshell (if the
quantum numbers identify a possible state).
If the Bohr model is used, what frequency of
light would be required for ionization of
hydrogen?
A.
B.
C.
D.
E.
A.
B.
C.
D.
E.
16. For electron distributions, which of the following
statements is/are true?
1.
2.
14
6.17  10 Hz
3
1.31  10 Hz
15
3.29  10 Hz
10
4.31  10 Hz
None of the above is within 5% of the
correct answer
3.
A.
B.
C.
D.
E.
d orbitals have a spherical shape.
p orbitals have a high electron density at
the nucleus.
s orbitals have no electron density at the
nucleus.
1 and 2
2 only
2 and 3
3 only
None of the statements is true
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WEEK 2: 4 SEP THRU 10 SEP; LECTURES 4-6
17. Which of the following represents an orbital in which a 3d electron could be found?
A.
B.
C.
D.
E.
1 only
2 only
4 only
1 and 5
2 and 3
18. An electron is in the 4s orbital of the hydrogen atom. Which one of these statements is(are) true?
i.
ii.
This hydrogen atom atom is in the ground state.
A hydrogen atom with an electron in the 4d orbital will be degenerate with the electron in the state
described above.
iii. A hydrogen atom with an electron in the 3s orbital will be degenerate with the electron in the state
described above.
A.
B.
C.
D.
E.
Week 2
only i is true.
only ii is true.
only iii is true.
ii and iii are true.
None of these are true.
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WEEK 2: 4 SEP THRU 10 SEP; LECTURES 4-6
Recitation Worksheet
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1. What is the wavelength of light that has a frequency of 6.2 × 109 Hz and in what region of the
electromagnetic spectrum can it be found?
-----------------------------------------------------------------------------------------------------------------------2. Which one of the following photons is higher in energy than a green photon?
A.
Microwave photon
B.
ultra-violet photon
C.
Red photon
D.
Radio frequency photon
-----------------------------------------------------------------------------------------------------------------------3. (A) What is the wavelength of one X-ray photon if the frequency is 1.00 × 1019 s−1?
(B) What is the energy of one X-ray photon of this frequency?
(C) What is the energy of one mole of X-ray photons of the same wavelength?
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4. There is a red emission line at 670nm in the line spectrum of Li. What is the energy difference
between the energy levels involved in the electronic transition that produces this emission
line?
A.
B.
C.
D.
2.97  10–19 J
6.70  10–7 J
4.48  1014 J
9.89  10–28 J
-----------------------------------------------------------------------------------------------------------------------5A. Which of the following electron transitions in a hydrogen atom will emit a photon, which
absorb a photon? (How do you know?)
A. n = 1 to n = 3
B. n = 4 to n = 3
C. n = 3 to n = 2
D. n = 3 to n = 1
E. n = 2 to n = 3
5B. Which of the above electron transitions in a hydrogen atom will result in emission of light
with the longest wavelength?
-----------------------------------------------------------------------------------------------------------------------6. Use the Bohr model and determine the wavelength of light that would ionize a hydrogen
atom if the electron were in an excited state (n =3). (Hint: ionization is the removal of an
electron; assume we are removing it from the n = 3 value)
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WEEK 2: 4 SEP THRU 10 SEP; LECTURES 4-6
-----------------------------------------------------------------------------------------------------------------------7A. An emission line the hydrogen atom has a wavelength of 93.8 nm. What region in the
electromagnetic spectrum is this emission found?
7B. Determine the final value of n associated with this emission? (Hint: Consider E = h and
the Rydberg equation, use this to find the value of nf.)
7C. Determine the initial value of n associated with this emission. (Hint: Will this value be
higher or lower than nf and why is this the case? What equation will you use to determine
this value; what values do you know?)
-----------------------------------------------------------------------------------------------------------------------8. Consider the rules for assigning quantum numbers.
Which is not a permissible set of quantum numbers?
Identify the orbital (if possible)
a)
n = 2, ℓ = 0, mℓ = 0
_____
b)
n = 3, ℓ = 2, mℓ = 2
_____
c)
n = 2, ℓ = 1, mℓ = 1
_____
d)
n = 3, ℓ = 3, mℓ = 0
_____
e)
n = 4, ℓ = 3, mℓ = 3
_____
Hint: What quantum number(s) gives the electron shell?
What quantum number number(s) indicate the subshell?
Which quantum number(s) define the orbitals in a subshell?
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9. Give the set of quantum numbers that describes each of the following orbitals assuming they
are all in the third shell.
A.
B.
C.
D.
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